IMI \(\mathcal {I}_{X\rightarrow Y}\)  represents
uncertainty reduction in \(Y\) 's future that comes from knowing only \(X\) 's
present as much as possible under the assumption of the Markov property with
respect to \(Y\)  and \(\overline{Y}\) . It should be noted here that this Markov
property has no physical relevance to the actual system \(Y\) , and is merely an
assumption that restricts the space of the minimization in Eq. () and so helps to provide an upper bound of
\(S(X_{t};Y_{t+\tau }|Y_{t})\) . IMI has been found to be
both a convenient and accurate bound on the secret key agreement rate
\(S(X_{t};Y_{t+\tau }|Y_{t})\)  [1]}, [2]}.
